Ebrahim Zolfaghari, spokesman for Iran's Khatam al-Anbiya Central Headquarters, dismissed US statements about vessel traffic as "baseless claims."
"As in the past, the Strait of Hormuz is under the full management and control of the Islamic Republic of Iran, and no commercial or oil tanker has had, nor will have, the possibility of secure transit through this strait without the permit and supervision of Iran's powerful armed forces," Zolfaghari said.
"The proud armed forces of Islamic Iran are monitoring all the movements of the American-Zionist enemies in the region," he added, saying Iran would respond to any threat at any level.
US President Donald Trump said Washington had "total control" of the Strait of Hormuz and warned that Iran could be "blown away" if Tehran chose to escalate.
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Trump's remarks came as Iran said the waterway would remain closed unless Washington accepted its conditions for ending the conflict.
Iranian security official Mohsen Rezaei said those conditions included the release of frozen Iranian assets and an end to conflicts elsewhere in the region, including Lebanon and Gaza.